Alternating direction methods – Optimization Online

A Dantzig-Wolfe Single-Level Reformulation for Mixed-Integer Linear Bilevel Optimization: Exact and Heuristic Approaches

Published: 2025/06/12

(Mixed) Integer Linear Programming, Bilevel Optimization, Branch and Cut Algorithms Alternating direction methods, Mixed integer linear bilevel optimization, penalty methods, primal heuristics, Single-level reformulations

Bilevel optimization problems arise in numerous real-world applications. While single-level reformulations are a common strategy for solving convex bilevel problems, such approaches usually fail when the follower’s problem includes integer variables. In this paper, we present the first single-level reformulation for mixed-integer linear bilevel optimization, which does not rely on the follower’s value function. Our … Read more

A Consensus-Based Alternating Direction Method for Mixed-Integer and PDE-Constrained Gas Transport Problems

Published: 2022/10/24, Updated: 2023/08/14

(Mixed) Integer Nonlinear Programming, Network Optimization, Optimization of Systems modeled by PDEs Alternating direction methods, gas transport networks, Graph decomposition, Mixed-integer nonlinear optimization, penalty methods

We consider dynamic gas transport optimization problems, which lead to large-scale and nonconvex mixed-integer nonlinear optimization problems (MINLPs) on graphs. Usually, the resulting instances are too challenging to be solved by state-of-the-art MINLP solvers. In this paper, we use graph decompositions to obtain multiple optimization problems on smaller blocks, which can be solved in parallel … Read more